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Tensor products of maximal Abelian subalgebras of C*-algebras

By S. Wassermann


It is shown that if C_1 and C_2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A_1 and A_2, respectively, then the completion of the algebraic tensor product of C_1 and C_2 in any C*-tensor product of A_1 and A_2 is maximal abelian provided that C_1 has the extension property of Kadison and Singer and C_2 contains an approximate identity for A_2. Examples are given to show that this result can fail if the conditions on the two masas do not both hold. This gives an answer to a long-standing question, but leaves open some other interesting problems, one of which turns out to have a potentially intriguing implication for the Kadison-Singer extension problem

Topics: QA Mathematics
Publisher: Cambridge University Press
Year: 2008
DOI identifier: 10.1017/S0017089508004151
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